62 citations · 265 across the 23 of their papers we have counts for
12 papers · 1 filter
Magnitude of module categories
Erlend D. Børve, Daniel Horiatakis, Martin Kalck
We define an invariant of the module category of a representation-finite algebra by the magnitude of its Auslander algebra. This invariant will be called the magnitude of the modul…
Cluster categories for completed infinity-gons I: Categorifying triangulations
İlke Çanakçı, Martin Kalck, Matthew Pressland
Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity-gons, which are discs with an infinite closed set of marked points on their boundary…
A finite dimensional algebra with a phantom (a corollary of an example by J. Krah)
Martin Kalck
We observe that there exists an associative finite dimensional -algebra of finite global dimension, such that the bounded derived category of finite dimens…
Relative singularity categories III: Cluster resolutions
Martin Kalck, Dong Yang
We build foundations of an approach to study canonical forms of -Calabi--Yau triangulated categories with cluster-tilting objects, using dg algebras and relative singularity cat…
Ringel duality for certain strongly quasi-hereditary algebras
Martin Kalck, Joseph Karmazyn
We introduce quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform fo…
A remark on Leclerc's Frobenius categories
Martin Kalck
Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that th…
Relative Singularity Categories
Martin Kalck
We study the following generalization of singularity categories. Let X be a quasi-projective Gorenstein scheme with isolated singularities and A a non-commutative resolution of sin…
Derived categories of graded gentle one-cycle algebras
Martin Kalck, Dong Yang
Let be a graded algebra. It is shown that the derived category of dg modules over (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orb…
Derived categories of quasi-hereditary algebras and their derived composition series
Martin Kalck
We study composition series of derived module categories in the sense of Angeleri Hügel, König & Liu for quasi-hereditary algebras. More precisely, we show that having a compositio…
Spherical subcategories in representation theory
Andreas Hochenegger, Martin Kalck, David Ploog
We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality…
Frobenius categories, Gorenstein algebras and rational surface singularities
Osamu Iyama, Martin Kalck, Michael Wemyss +1
We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result…
Singularity categories of gentle algebras
Martin Kalck
We determine the singularity category of an arbitrary finite dimensional gentle algebra . It is a finite product of -cluster categories of type . Equivalently…